Timeline for Constant "periodization" of a function
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2018 at 10:24 | comment | added | Rodrigo | Indeed if you assume say that $w$ is also smooth this periodization equals $\sum \hat w(n) e(n x)$, so the condition is equivalent to $\hat w(n) = 0$ at any integer $n$ (so the Fourier transform of any smooth rapidly decreasing function that is zero at integers gives a counter-example and these are essentially all of them). | |
| Oct 15, 2018 at 8:58 | vote | accept | Matthias Ludewig | ||
| Oct 15, 2018 at 8:53 | comment | added | Matthias Ludewig | Jupp, for example. But since the function is rapidly decaying, you can choose any enumeration of the integers and end up with the same value. | |
| Oct 15, 2018 at 6:46 | answer | added | Dirk | timeline score: 6 | |
| Oct 15, 2018 at 6:42 | comment | added | Gerry Myerson | The sum over the integers is a doubly-infinite series. How are you defining its value? Something like $\lim_{m\to\infty}\sum_{-m}^m$? | |
| Oct 15, 2018 at 6:34 | history | asked | Matthias Ludewig | CC BY-SA 4.0 |